A different workflow, that would make it much easier to run things locally with the exact same software versions that are used remotely, would be to switch to using docker container images to bundle stan, R, c++ compilers, etc, rather than bundling them into AMI virtual machine images, as mentioned briefly by mbjospeh:
A downside of doing this would be the additional learning curve of getting some familiarity with docker. This container-image based workflow is used by many software development teams as one piece of the puzzle in managing software dependencies to ensure that the versions of software that are developed and tested locally in development environments are the exact same versions that gets deployed (to AWS or wherever) and run.